Research
Bridge gaps among Geology, Geophysics, & Computer ScienceImage processing, Machine learning, Seismic interpretation, Subsurface modeling, Geophysical inversion, Computer graphics…. 
Note: we compute and display all the results using our freely available Java packages (etc., Mines JTK).
Channel simulation–I am running Dr. Zoltán Sylvester‘s codes to simulate the following beautiful river meandering. I am learning from Dr. Sylvester to build 3D realistic channel models. 

Forward stratigraphic modeling–it might be a good time for a geophysicist to start working on some geologic problems as well:) The following animation shows my simple implementation of a 2D stratigraphic simulation. collaborating with geology experts including Dr. Jinyu Zhang, Dr. Zoltán Sylvester and Dr. Jacob Covault. 

Parameterize 3D folding and faulting–a workflow to automatically create numerous realistic structure models! It took me quite some time to write software for the 3D visualization (even more time if without Mines JTK), but I enjoyed working on it:) 
FaultNet3D: predicting fault probabilities, strikes and dips with a common CNNClick the above figure to view highresolution images:) Collaborators: Yunzhi Shi and Sergey Fomel at UT Austin, TX, USA Luming Liang at Uber, CO, USA Qie Zhang and Anar Z. Yusifov at BP American Inc., TX, USA Journal paper is in submission. SEG abstract accepted: Wu, X., Y. Shi, S. Fomel, and L. Liang, Convolutional neural network for fault interpretation in seismic images. 88th SEG, Expanded Abstracts. [PDF] This work will be presented at SEG 2018. (I gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research!) 
FaultSeg: using synthetic datasets to train an endtoend CNN for 3D fault segmentationClick the above figure to view highresolution images:) More tests on SEG open datasets:Kerry3D; Opunake3D, … Wu, X., L. Liang (Uber), Y. Shi and S. Fomel, 2019, FaultSeg3D: using synthetic datasets to train an endtoend CNN for 3D fault segmentation. Geophysics, in press. [CODE]. 
Toward accurate seismic flatteningA input seismic image (a) with complicated structures, conventional flattening with slopes (b), improved flattening (c) with the proposed accurate flattening method, and horizons (d) computed by the improved flattening. This method works well in 3D as in (e), (f) and (g). No fault information is used as constraints in these examples. Click the above figure to view highresolution images. Coming soon… This work will be presented at TCCS fall sponsor meeting, 2018. 
]Normal fault populations in the Costa Rica Margin (NSF project, collaborate with Dr. Nathan Bangs)From the 3D seismic image (right above) acquired in Costa Rica subduction area (left above), we automatically compute more than 30 thousands 3D fault surfaces and their strikes, dips, and slips. With these computed highresolution fault strikes, we are able to make the “blooming roses” (the cartoon below) to visualize the faultstrike variations with depth (or geologic time) and space.

Automatic fault interpretation with optimal surface votingFrom an input image (a) of seismic discontinuity (1planarity) attribute, we first compute a voting score map (b), from which fault surfaces (colored by fault strikes in (c)) are then automatically extracted. This work will be presented at SEG 2018. 
Leastsquares horizons with local slopes and multigrid correlationsFrom a 3D seismic image (a), two horizon surfaces (colored by seismic amplitude) are automatically computed with one (b) and two (c) control points (colored by green in (b) and (c)). Wu, X. and S. Fomel, 2018, Leastsquares horizons with local slopes and multigrid correlations, Geophysics, Vol. 83(4), IM29IM40. [PDF] [CODE] This work will be presented at SEG 2018. 
Fast salt boundary interpretation with optimal path pickingSalt boundary interpretation is a crucial step for velocitymodel building in seismic migration, but re mains a big challenge for automatic methods and a highly laborintensive task for manual interpretation. We propose a semiautomatic method to efficiently and accurately extract 2D and 3D complicated salt boundaries from seismic envelope images. In 2D salt boundary extraction, we first pick a few points to interpolate an initial curve that is close to the true salt boundary. These points are picked near the salt boundary but are not required to be exactly on the boundary, which makes human interactions convenient and efficient. We then resample the envelope image in a band area centered at the initial curve to obtain a new image where the true salt boundary is an open curve extending from left to right. We then extract the salt boundary in the new image using an optimalpath picking algorithm, which is robust to track a highly discontinuous salt boundary by picking the optimal path with globally maximum envelope values. We finally map the picked path back to the original image to obtain a final salt boundary. In 3D salt boundary extraction, we apply the 2D method to recursively pick 2D salt boundaries in a sequence of inline or crossline slices and then fit these 2D boundaries to obtain a 3D surface of the salt boundary. In this proposed recursive picking, human interactions are greatly reduced by using a salt boundary picked in the previous slice as an initial curve for picking in a followed slice.
Wu, X., S. Fomel, and M. Hudec, 2017, Fast salt boundary interpretation with optimal path picking. Geophysics,

Incremental correlation of multiple well logs following geologically optimal neighbors
Welllog correlation is a crucial step to construct cross sections in estimating structures between wells and building subsurface models. Manually correlating multiple logs can be highly subjective and laborintensive. We propose a weighted incremental correlation method to efficiently correlate multiple well logs following a geologically optimal path. In this method, we first automatically compute an optimal path that starts with longer logs and follows geologically more continuous structures. We then use the dynamic warping technique to sequentially correlate the logs following the path. To avoid potential error propagation with the path, we modify the dynamic warping algorithm to use all the previously correlated logs as references to correlate the current log in the path. During the sequential correlations, we compute geologic distances between the current log and all the reference logs. Such distances are proportional to Euclidean distances but increase dramatically across discontinuous structures such as faults and unconformities that separate the current log from the reference logs. We also compute correlation confidences to provide quantitatively quality control of the correlation results. We use both the geologic distances and correlation confidences to weight the references in correlating the current log. By using this weighted incremental correlation method, each log is optimally correlated to all the logs that are geologically closer and are ordered with higher priorities in the path. Hundreds of well logs from the Teapot Dome survey demonstrate the efficiency and robustness of the method.
Wu, X., Y. Shi, S. Fomel, and F. Li, 2018, Incremental correlation of multiple well logs following geologically optimal neighbors. Interpretation, Vol. 6(3), T713T722. [PDF] 
Directional structure tensors in estimating seismic structural and stratigraphic orientations
Conventional structuretensor method often generates significant errors in estimating orientations of the reflections with steep and rapidly varying slopes. To better estimate reflection orientations, we propose to construct structure tensors in a new space, where the reflections are mostly flat or only slightly dipping and the variation of reflection slopes is reduced. We use these constructed structure tensors to compute reflection normals in this new space and then transform the normals back to obtain a better estimation of reflection orientations in the original space. Seismic stratigraphic features such as channels are often aligned within dipping reflections. It is not discussed previously by others to estimate orientations of such features directly from a seismic image. An ideal way to estimate stratigraphic orientations is to first extract a horizon surface with stratigraphic features, and then construct structure tensors with gradients on the surface to estimate the orientations of the features. However, extracting horizon surfaces can be a difficult and timeconsuming task in practice. Fortunately, computing gradients on a horizon surface is only a local operation and is equivalent to directly compute directional derivatives along reflection slopes without picking horizons. Based on this observation, we propose to use an equivalent but more efficient way to estimate seismic stratigraphic orientations by using structure tensors constructed with the directional derivatives along reflections. Wu, X. and X., Janson, 2017, Directional structure tensors in estimating seismic structural and stratigraphic orientations. Geophysical Journal International, Vol. 210(1), 534548. [PDF] 
Efficient structure and stratigraphyoriented smoothing to simultaneously enhance reflections, faults and channels
In this paper, I propose methods to enhance seismic reflections, faults, and channels and simultaneously obtain mappings of faults and channels. In the methods, I first estimate orientations of reflections, faults, and channels directly from a seismic image. I then use the estimated orientations to control smoothing directions in an efficient iterative diffusion scheme to smooth a seismic image along reflections and channels. In this iterative scheme, I also efficiently compute mappings of faults and channels, which are used to control smoothing extents in the diffusion to stop smoothing across faults and channels. This diffusion scheme iteratively smoothes a seismic image along reflections and channels while at the same time updating the mappings of faults and channels. After a small number of diffusion steps, I finally obtain enhanced mappings of faults and channels and a smoothed seismic image with enhanced reflections, faults, and channels. Wu, X., 2016, Efficient structure and stratigraphyoriented smoothing to simultaneously enhance seismic reflections, faults, and channels. Geophysical prospecting, submitted. 
Structure, stratigraphy, and faultguided regularization in geophysical inversion
Geophysical inversion is often illposed because of inaccurate and insufficient data. Regularization is often applied to the inversion problem to obtain a stable solution by imposing additional constraints on the model. Common regularization schemes impose isotropic smoothness on solutions and may have difficulties in obtaining geologically reasonable models that are often supposed to be anisotropic and conform to subsurface structural and stratigraphic features. I introduce a general method to incorporate constraints of seismic structural and stratigraphic orientations and fault slips into geophysical inversion problems. I first use a migrated seismic image to estimate structural and stratigraphic orientations and fault slip vectors that correlate fault blocks on opposite sides of a fault. I then use the estimated orientations and fault slips to construct simple and convenient anisotropic regularization operators in inversion problems to spread information along structural and stratigraphic orientations and across faults. In this way, we are able to compute inverted models that conform to seismic reflectors, faults, and stratigraphic features such as channels. The regularization is also helpful to integrate welllog properties into the inversion by spreading the measured rock properties away from the welllog positions into the whole inverted model across faults and along structural and stratigraphic orientations. I use a 3D synthetic example of impedance inversion to illustrate the structure, stratigraphy, and faultguided regularization method. I further applied the method to estimate seismic interval velocity and to compute structure and stratigraphyoriented semblance. Wu, X. , 2017, Structure, stratigraphy, and faultguided regularization in geophysical inversion. Geophysical Journal International, Vol. 210(1), 184195. [PDF] 
Improved horizon extraction and seismic attributes for seismic geomorphology analysis of carbonate systems
Directional structuretensor based coherence to detect seismic channels and faults
A coherence image can be computed from the eigenvalues of conventional structure tenors, which are outer products of gradients of a seismic image. I propose a simple but effective method to improve such a coherence image by using directional structure tensors, which are different from the conventional structure tensors in only two aspects. Firstly, instead of using image gradients with vertical and horizontal derivatives, I use directional derivatives, computed in directions perpendicular and parallel to seismic structures (reflectors), to construct directional structure tensors. With these directional derivatives, lateral seismic discontinuities, especially those subtle stratigraphic features aligned within dipping structures, can be better captured in the structure tensors. Secondly, instead of applying Gaussian smoothing to each element of the constructed structure tensors, I apply approximately fault and stratigraphyoriented smoothing to enhance the lateral discontinuities corresponding to faults and stratigraphic features in the structure tensors. Wu, X., 2016, Directional structuretensor based coherence to detect seismic channels and faults. Geophysics, 82(2), A13A17. [PDF] 
Methods to enhance seismic faults and construct fault surfaces
We propose a method to enhance a precomputed fault attribute image, and simultaneously estimate fault strikes and dips. In this enhanced image, image features are smoothed along fault orientations so that the features unrelated to faults are suppressed while those fault features are more continuous and prominent. We then compute fault samples on the ridges of an enhanced fault attribute image. Each fault sample corresponds to one and only one seismic image sample and is oriented by the estimated fault strike and dip. Fault surfaces can be constructed by directly linking the oriented fault samples with consistent fault strikes and dips. For complicated cases with missing fault samples and noisy samples, we further propose to use a perceptual grouping method to infer fault surfaces that reasonably fit the positions and orientations of the fault samples. We apply these methods to 3D synthetic and real examples and successfully extract multiple intersecting fault surfaces and complete fault surfaces without holes. Wu, X. and Z. Zhu 2017, Methods to enhance seismic faults and construct fault surfaces. Computer & Geosciences, Vol. 107, 3748. 
Building 3D subsurface models conform to seismic horizons, faults, unconformities, and stratigraphic features
I propose an automatic method to fully use both seismic and borehole data to build subsurface models that honor borehole measurements and conform to seismic horizons, faults, unconformities, and stratigraphic features such as channels. In this method, I first automatically remove the faulting and folding in both seismic and borehole data and map them into a flattened space, in which seismic reflectors and borehole measurements corresponding to the same geologic layers are horizontally aligned. I then build a subsurface model in this flattened space by computing a sequence of 2D horizontal interpolations of well logs. Each horizontal interpolation is guided by the stratigraphic features apparent in the corresponding horizontal seismic slice, so that the interpolant conforms to the seismic stratigraphic features. I finally map the interpolated model back into the input space and obtain a subsurface model that honors both the seismic and borehole data. Wu, X., 2016, 3D seismic image processing for subsurface modeling. Geophysics, 82(3), IM21IM30. [PDF] 
Methods to compute salt likelihoods and extract salt boundaries from 3D seismic images
From a 3D seismic image, I first efficiently compute a salt likelihood image, in which the ridges of likelihood values indicate locations of salt boundaries. I then extract salt samples on the ridges. These samples can be directly connected to construct salt boundaries in cases when salt structures are simple and the boundaries are clean. In more complicated cases, these samples may be noisy and incomplete, and some of the samples can be outliers unrelated to salt boundaries. Therefore, I finally develop a method to accurately fit noisy salt samples, reasonably fill gaps, and handle outliers to simultaneously construct multiple salt boundaries. In this step of constructing salt boundaries, I also propose a convenient way to incorporate human interactions to obtain more accurate salt boundaries in especially complicated cases. Wu, X., 2016, Methods to compute salt likelihoods and extract salt boundaries from 3D seismic images. Geophysics, 81(6), IM119IM126. [PDF] 
Simultaneous multiple wellseismic ties with flattened synthetic and real seismograms
Numerous methods have been proposed to compute wellseismic ties by correlating real seismograms with synthetic seismograms computed from velocity and density logs. However, most methods tie multiple wells to seismic data onebyone, hence do not guarantee lateral consistency among multiple well ties. We propose to simultaneously tie multiple wells by first flattening synthetic and real seismograms so that all seismic reflectors are horizontally aligned. By doing this, we turn multiple wellseismic tying into a 1D correlation problem. We then simply compute only verticallyvariant but laterallyconstant shifts to correlate these horizontally aligned (flattened) synthetic and real seismograms. This twostep correlation method maintains lateral consistency among multiple well ties by computing a laterally and vertically optimized correlation of all synthetic and real seismograms. Wu, X. and G. Caumon, 2017, Simultaneous multiple wellseismic ties with flattened synthetic and real seismograms. Geophysics, Vol. 82(1), IM13IM20.. [PDF] 
Automatically interpreting all faults, unconformities, and horizons from 3D seismic images
We have proposed a processing procedure to automatically extract all the faults, unconformities, and horizon surfaces from a 3D seismic image. In our processing, we first extracted fault surfaces, estimated fault slips, and undid the faulting in the seismic image. Then, we extracted unconformities from the unfaulted image with continuous reflectors across faults. Finally, we used the unconformities as constraints for image flattening and horizon extraction. Most of the processing was image processing or array processing and was achieved by efficiently solving partial differential equations. Wu, X. and D. Hale, 2016, Automatically interpreting all faults, unconformities, and horizons from 3D seismic images. Interpretation, 4(2), 111. [Link] [PDF] 
Moving faults while unfaulting 3D seismic images
We developed two methods to compute vector shifts that simultaneously move fault blocks and the faults themselves to obtain an unfaulted image with minimal distortions. For both methods, we use estimated fault positions and slip vectors to construct unfaulting equations for image samples alongside faults, and we construct simple partial differential equations for samples away from faults. We solve these two different kinds of equations simultaneously to compute unfaulting vector shifts that are continuous everywhere except at faults. Wu, X., S. Luo, and D. Hale, 2016, Moving faults while unfaulting 3D seismic images. CWP Report 839. [Link] Technical talk: https://www.youtube.com/watch?v=gDxfLuYf3C8 
3D seismic image processing for faults
Numerous methods have been proposed to automatically extract fault surfaces from 3D seismic images, and those surfaces are often represented by meshes of triangles or quadrilaterals. Such mesh data structures are more complex than the arrays used to represent seismic images, and are more complex than necessary for subsequent processing tasks, such as that of automatically estimating fault slip vectors. To facilitate image processing for faults, we propose a simpler linked data structure in which each sample of a fault corresponds to exactly one image sample. Using this linked data structure, we extracted multiple intersecting fault surfaces from 3D seismic images. We then used the same structure in subsequent processing to estimate fault slip vectors, and to assess the accuracy of estimated slips by unfaulting the seismic images.
Wu, X. and D. Hale, 2016, 3D seismic image processing for faults. CWP Report 838. [Link] Technical talk: https://www.youtube.com/watch?v=wp6Vhv3BxBE 
3D seismic image processing for unconformities
We propose a 3D seismic unconformity attribute to detect complete unconformities, highlighting both their termination areas and correlative conformities. We then extract unconformity surfaces on the ridges of the unconformity attribute image. These detected unconformities are further used as constraints to more accurately estimate seismic normal vectors at unconformities. Then, using seismic normal vectors and detected unconformities as constraints, we can better flatten seismic images containing unconformities.
Wu, X. and D. Hale, 2015, 3D seismic image processing for unconformities. CWP Report 813. [Link] Technical talk: https://www.youtube.com/watch?v=RjhtCvexHhY 
Horizon volumes with interpreted constraints
We propose two methods for constructing seismic horizons aligned with reflectors in a 3D seismic image. The first method extracts horizons one at a time; the second generates at once an entire volume of horizons. The most significant new aspect of both methods is the ability to specify, perhaps interactively during interpretation, a small number of control points that may be scattered through out a 3D seismic image. Examples show that control points enable the accurate extraction of horizons from seismic images in which noise, unconformities, and faults are apparent. These points represent constraints that we implement simply as preconditioners in the conjugate gradient method used to construct horizons. Wu, X. and D. Hale, 2015, Horizon volumes with interpreted constraints. CWP Report 812. [Link] Technical talk: https://www.youtube.com/watch?v=w6wtf20OwCM 
Extracting horizons and sequence boundaries from 3D seismic images
We first introduce a globally optimal method to efficiently extract a horizon from a seismic image. We then use scattered control points as constraints to enable our horizonextraction method to extract sequence boundaries. Finally, we propose an activesurface method to refine the globally optimized horizons to align with amplitude peaks or troughs and thereby reveal more geologic details. Wu, X. and D. Hale, 2013, Extracting horizons and sequence boundaries from 3D seismic images. 83rd Annual Meeting of the Society of Exploration Geophysics, Expanded Abstracts. [Link] Wu, X. and D. Hale, 2013, Extracting horizons and sequence boundaries from 3D seismic images. CWP Report 766. [Link] Technical talk: https://www.youtube.com/watch?v=0vNoM4c3E0 
Generating a relative geologic time volume by improved 3D graphcutbased phase unwrapping method with horizon and unconformity constraints
We propose a robust phase unwrapping method to compute a relative geologic time volume from a 3D seismic instantaneous phase volume. We provide a convenient way to incorporate interpreted horizons and unconformities into our phase unwrapping method to obtain more reliable results in cases complicated by noise, faults, and unconformities. Using a computed RGT volume, we further automatically generate a 3D seismic Wheeler volume.
